Rings of low rank with a standard involution

Details Rings of low rank with a standard involution Rings of low rank with a standard involution

2010-03-18

arxiv.org/abs/1003.3512v2

Mathematics

Number Theory

17 pages; minor revisions

Scientific paper

We consider the problem of classifying (possibly noncommutative) R-algebras of low rank over an arbitrary base ring R. We first classify algebras by their degree, and we relate the class of algebras of degree 2 to algebras with a standard involution. We then investigate a class of exceptional rings of degree 2 which occur in every rank n >= 1 and show that they essentially characterize all algebras of degree 2 and rank 3.

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